Gas turbine systems are one example of turbomachines widely utilized in fields such as power generation. A conventional gas turbine system includes a compressor section, a combustor section, and a turbine section. During operation of the gas turbine system, various components in the system are subjected to high temperature flows, which can cause the components to fail. Since higher temperature flows generally result in increased performance, efficiency, and power output of the gas turbine system, it may be desirable to cool the components that are subjected to high temperature flows to allow the gas turbine system to operate at increased temperatures.
Many system requirements are instituted for each stage of the turbine section, or hot gas path section, of a gas turbine system in order to meet design goals including overall improved efficiency and airfoil loading. Particularly, the buckets of the first stage of the turbine section are designed meet the operating requirements for that particular stage and also meet requirements for bucket cooling area and wall thickness. However, conventional designs fail to meet these operating requirements in some cases.